Tip the sugar into a pan with 250ml water. Bring to the boil slowly, ensuring the sugar is fully dissolved. Add the chopped peaches and cook until very soft. Remove from the heat, mash the peaches with a fork, and leave to infuse for 1 hr.
Sieve the syrup through a fine sieve into a jug, mashing the fruit to release all the liquid. The syrup will keep in the fridge for one week.
Put the teabags in a large heatproof jug and pour over 2 litres boiling water. Leave to steep for 4 mins, then carefully remove the teabags. Leave to cool, then transfer to the fridge until chilled.
Stir the peach syrup into the iced tea with some ice, or pour a little of the syrup into tall glasses and add the tea. Top up with more water, sparkling water or ice. Add peach slices to serve.